When designing a Plane. What would be a good ratio between prop size and plane width?
Optimal prop diameter depends solely on a propeller shape, blade count, design speed and motor parameters. You should also check low speed thrust for takeoff performance.
For example I have a plane (not flown yet) with 3m wingspan and 2 folding props that are over 40cm. IIRC 15x10 but with slightly larger hubs. They are (IMHO too) large and were chosen to maximize the range.
In general larger props can be more efficient, but also have more risk of hitting the ground or (in a twin) the fuselage. Also, you may not find motors in the right Kv for a particular prop diameter/pitch and battery voltage.
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Exactly, in case of the plane I am working on my predecessors decided to use folding props to address hitting the ground. Now we need guide rods to make sure props won’t get stuck on the wings.